Reynolds Equation and Mixing Length Model

Equation (10) is referred to as the Reynolds equation. The term  is the stress induced by the turbulent fluctuation. i.e.,

(12)

Equation (10) may be restated as

(13)

where  is the mean viscous stress tensor and  is the turbulent stress tensor.

The Reynolds stress (turbulent stress) is a symmetric tensor and its components are given by

(14)

Note that the turbulent stresses introduce six additional unknowns into the averaged Navier-Stokes equation.